论文标题
通过超图分解链接的群集扩展
Linked Cluster Expansions via Hypergraph Decompositions
论文作者
论文摘要
我们提出了一项超图扩展，该扩展通过扰动连接的群集扩展，促进了通过多个位点相互作用的量子自旋模型的直接处理。主要思想是生成所有相关的子集群，并将它们整理成基本上受超图同构基本支配的等效类。具体而言，使用高图的könig表示，用于使图形同构访问等效关系。在此过程中，我们确定每个等价类别的嵌入因子，该类别用于最终重新召集以获得最终结果。作为一个有启发性的例子，我们计算了三维立方晶格上横向场中的平板能量和特定的激发差距。
We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into equivalence classes essentially governed by hypergraph isomorphism. Concretely, a reduced König representation of the hypergraphs is used to make the equivalence relation accessible by graph isomorphism. During this procedure we determine the embedding factor for each equivalence class, which is used in the final resummation in order to obtain the final result. As an instructive example we calculate the ground-state energy and a particular excitation gap of the plaquette Ising model in a transverse field on the three-dimensional cubic lattice.
